Geodesic
On the de Rham complex on a scale of anisotropic weighted H\"older spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 428-444

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We obtain a solvabilty criterion for the operator equations induced by de Rham differentials on a scale of anisotropic weighted Hölder spaces on the strip $\mathbb{R}^n \times [0,T]$, $n\geq 1$, where the weight controls the behavior of elements at the infinity point with respect to the space variables. Besides, we give a description of the closures in these space of the set of infinitely differentiable functions on the strip $\mathbb{R}^n \times [0,T]$ that are compactly supported with respect to the space variables. The results are applied to study the properties of the famous Leray-Helmholtz projection from the theory of the Navier-Stokes equations on the scale of these weighted spaces for $n\geq 2$.
Keywords: weighted Hölder spaces, de Rham complex. 
@article{SEMR_2020_17_a128,
     author = {K. V. Gagelgans and A. A. Shlapunov},
     title = {On the de {Rham} complex on a scale of anisotropic weighted {H\"older} spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {428--444},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a128/}
}
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K. V. Gagelgans; A. A. Shlapunov. On the de Rham complex on a scale of anisotropic weighted H\"older spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 428-444. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a128/